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on Economic Design |
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Issue of 2022‒09‒19
four papers chosen by Guillaume Haeringer, Baruch College and Alex Teytelboym, University of Oxford |
| By: | Rangeet Bhattacharyya; Palash Dey; Swaprava Nath |
| Abstract: | The auction of a single indivisible item is one of the most celebrated problems in mechanism design with transfers. Despite its simplicity, it provides arguably the cleanest and most insightful results in the literature. When the information of the auction is available to every participant, Myerson [17] provided a seminal result to characterize the incentive-compatible auctions along with revenue optimality. However, such a result does not hold in an auction on a network, where the information of the auction is spread via the agents, and they need incentives to forward the information. In recent times, a few auctions (e.g., [10, 15]) were designed that appropriately incentivize the intermediate nodes on the network to promulgate the information to potentially more valuable bidders. In this paper, we provide a Myerson-like characterization of incentive-compatible auctions on a network and show that the currently known auctions fall within this larger class of randomized auctions. We obtain the structure of the revenue optimal auction for i.i.d. bidders on arbitrary trees. We discuss the possibilities of addressing more general settings. Through experiments, we show that auctions following this characterization can provide a higher revenue than the currently known auctions on networks. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.09326&r= |
| By: | Anindya Bhattacharya; Debapriya Sen |
| Abstract: | We study some problems of collective choice when individuals can have expressive preferences, that is, where a decision-maker may care not only about the material benefit from choosing an action but also about some intrinsic morality of the action or whether the action conforms to some identity-marker of the decision-maker. We construct a simple framework for analyzing mechanism design problems with such preferences and present some results focussing on the phenomenon we call "Brexit anomaly". The main findings are that while deterministic mechanisms are quite susceptible to Brexit anomaly, even with stringent domain restriction, random mechanisms assure more positive results. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.09851&r= |
| By: | Wesley H. Holliday; Eric Pacuit; Saam Zahedian |
| Abstract: | In social choice theory, voting methods can be classified by invariance properties: a voting method is said to be C1 if it selects the same winners for any two profiles of voter preferences that produce the same majority graph on the set of candidates; a voting method is said to be pairwise if it selects the same winners for any two preference profiles that produce the same weighted majority graph on the set of candidates; and other intermediate classifications are possible. As there are far fewer majority graphs or weighted majority graphs than there are preference profiles (for a bounded number of candidates and voters), computer-aided techniques such as satisfiability solving become practical for proving results about C1 and pairwise methods. In this paper, we develop an approach to generalizing impossibility theorems proved for C1 or pairwise voting methods to impossibility theorems covering all voting methods. We apply this approach to impossibility theorems involving "variable candidate" axioms--in particular, social choice versions of Sen's well-known $\gamma$ and $\alpha$ axioms for individual choice--which concern what happens when a candidate is added or removed from an election. A key tool is a construction of preference profiles from majority graphs and weighted majority graphs that differs from the classic constructions of McGarvey and Debord, especially in better commutative behavior with respect to other operations on profiles. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.06907&r= |
| By: | Francesco Giovannoni; Toomas Hinnosaar |
| Abstract: | We study a buyer-seller problem of a novel good for which the seller does not yet know the production cost. A contract can be agreed upon at either the ex-ante stage, before learning the cost, or at the ex-post stage, when both parties will incur a costly delay, but the seller knows the production cost. We show that the optimal ex-ante contract for a profit-maximizing seller is a fixed price contract with an "at-will" clause: the seller can choose to cancel the contract upon discovering her production cost. However, sometimes the seller can do better by offering a guaranteed-delivery price at the ex-ante stage and a second price at the ex-post stage if the buyer rejects the first offer. Such a "limited commitment" mechanism can raise profits, allowing the seller to make the allocation partially dependent on the cost while not requiring it to be embedded in the contract terms. Analogous results hold in a model where the buyer does not know her valuation ex-ante and offers a procurement contract to a seller. |
| Date: | 2022–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2208.04985&r= |